Optimal auctions with multidimensional types and the desirability of exclusion

Within the context of a single-unit, independent private values auction model, we show that if bidder types are multidimensional, then under the optimal auction exclusion of a positive measure of bidder types occur. The results complements Armstrong’s (1996) exclusion of types result.     

Characterization of bidding behavior in multi-unit auctions

This paper considers a very general class of single or multi-unit auctions of indivisible objects. The model allows for interdependent values, multidiminensional types and any attitude towards risk. Assuming only optimal behavior, we prove that each bid is chosen in order to equalize the marginal benefit to the marginal cost of bidding. This generalizes many existing results in the literature. We use this characterization to obtain sufficient conditions for truthful bidding, monotonic best reply strategies and identification results for multi-unit auctions.     

The use of bundling in B2B online reverse auctions

In industrial purchasing a request for quotation (RFQ) can consist of a single item, but is most often composed of two or more products and/or services bundled together. While such bundles are used in offline purchase negotiations, their criticality is heightened in online auctions due to their usual short duration and constrained bidding environment. Despite this importance, little systematic discussion or evaluation has taken place concerning bundling practice, especially as it relates to the individual items included in the bundle, the overall bundle composition, and the resulting supply base and ultimate bundle performance. This study investigates these issues by developing a conceptual model and testing it with a large-scale survey completed by purchasing professionals practicing bundling in B2B online auctions. Results indicate that crafting a more homogeneous bundle is most important in achieving a successful outcome. Furthermore, more complex or difficult-to-specify items do not impact perceived bundle performance, but do influence the supply base that is willing and able to bid on the business.     

Detection of collusion in government procurement auctions

Research on bidder collusion in procurement auctions is reasonably successful in unveiling the mechanisms of collusion among the bidders. But it is relatively weak in forwarding effective practical methods of collusion detection before the winner is declared, because they presuppose the knowledge of collusion in specific auctions. Past studies, however, point out the need for working with bid price-to-reserve price ratios rather than bid prices or winning bid prices, to be free from the problem of heteroscedasticity. They also draw an important inference that the set of collusive data are significantly different from the set of competitive data. On the basis of these basic facts, the current paper outlines a seven-step approach to collusion detection. The approach makes rudimentary statistical analysis of bid price-to-reserve price ratios for all the bidders. The analysis comprises tests of equality of means, medians and variance and tests of skewness, autocorrelation and normality of the ratios. It divides the ratios into two significantly different clusters. The cluster with the higher mean and variance values of the ratios corresponds to collusive bidding with the other cluster corresponding to competitive bidding. The paper proposes the construction of a process control chart to detect occurrence of collusion in an auction immediately after the price bids are opened. The approach is illustrated by applying it to data from procurement auctions for construction projects in a State Department of the Republic of India.     

When does defection pay?

The present paper investigates cluster adjustment to changing economic environments by focussing on the role and stability of institutional arrangements in their local culture. It postulates two idealtypical local cultures where firms act in the common (collective) or in their own interest (egoistic). By comparing adjustment performance and stability for both types, the model finds that clusters in very volatile environments are unlikely to exhibit collective local cultures as these are unstable and provide only limited benefits for adjustment performance. Clusters facing more stable environments are more likely to show collective local cultures as these increase adjustment performance and are more stable against individual defection. Both findings suggest that collective local cultures in clusters can be relatively stable for limited environment volatility.     

A general construction of E(s 2)-optimal large supersaturated designs

A general method for construction of E(s ²)-optimal, two-level supersaturated designs (SSDs) with the equal occurrence property, from supplementary difference sets is introduced. It is proved that SSDs constructed in this way are E(s ²)-optimal. Comparisons are made with previous works and it is shown that the proposed method gives promising results for the construction of E(s ²)-optimal large SSDs.     

On the lowest-winning-bid and the highest-losing-bid auctions

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n−k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner.     

The <Emphasis Type="Italic">K</Emphasis><Subscript>ϕ</Subscript>-Divergence Statistic for Categorical Data Problems

In this work a new family of statistics based on K _ϕ -divergence (Burbea and Rao (1982) On the convexity of divergence measures based on entropy function. IEEE Trans Inf Theory 28, 489–495) are obtained by either replacing both distributions involved in the argument by their samples estimates or replacing one distribution and considering the other as given. Asymptotic distributions of these statistics are obtained and test for goodness-of-fit and for homogeneity with a known distribution, can be constructed on the basis of these results     

Minimal efficiency of designs under the class of orthogonally invariant information criteria

Consider the linear regression model with uncorrelated errors and an experimental design . In the article, we address the problem of calculating the minimal efficiency of with respect to the class of orthogonally invariant information criteria, containing all Kiefers criteria of _p-optimality, among others. We show that the -minimal efficiency of is equal to the minimal efficiency of with respect to a finite class of criteria which generalize the criterion of E-optimality. We also formulate conditions under which a design is maximin efficient, i.e. the most efficiency-stable for criteria from . To illustrate the results, we calculated the -minimal efficiency of _p (in particular D, A and E) optimal designs for polynomial regression on [–1,1] up to degree 4. Moreover, for the quadratic model we explicitly constructed the -maximin efficient design.Acknowledgement. The author would like to thank prof. Pázman as well as an anonymous referee for useful and inspiring comments on earlier versions of this article.Supported by: VEGA grant of the Slovak Agency No. 1/0264/03     

Some general results for moments in bivariate distributions

The purpose of this paper is to present a closed formula to compute the moments of a general function from the knowledge of its bivariate survival function. The result is derived by utilizing an integration by parts formula for two variables, which is not readily available in the literature. Many of the existing results are obtained as special cases. Finally, two examples are presented to illustrate the results. In both the examples, mixed moments as well as moments for the series system and parallel system are obtained. The integration by parts formula in two variables, derived here, is of interest in its own right and we hope that it will be useful in other investigations. The integration by parts formula in two variables is derived as a special case of a general formula in n variables.     

Modelling optimal strategies for the allocation of wealth in multicurrency investments

This paper analyzes rates of return on financial assets denominated in five major currencies and provides a framework for the determination of optimal strategies for the allocation of wealth in multicurrency investments. Three models are estimated: a univariate autoregressive conditional heteroskedasticity (ARCH) model, an extended ARCH model using the random coefficient (RC) procedure, and a pure RC model. A comparison of the forecasts of these models with those generated by a random walk model demonstrates that forecasts based on the RC/extended ARCH procedure are superior to those based on the random walk model and those based on direct ARCH estimation. These results could be useful for both international investors for the allocation of their wealth among fixed-income investment securities and central banks for the management of their external reserve assets.     

Comparison of Hypothesis Testing and Bayesian Model Selection

The main goal of both Bayesian model selection and classical hypotheses testing is to make inferences with respect to the state of affairs in a population of interest. The main differences between both approaches are the explicit use of prior information by Bayesians, and the explicit use of null distributions by the classicists. Formalization of prior information in prior distributions is often difficult. In this paper two practical approaches (encompassing priors and training data) to specify prior distributions will be presented. The computation of null distributions is relatively easy. However, as will be illustrated, a straightforward interpretation of the resulting p-values is not always easy. Bayesian model selection can be used to compute posterior probabilities for each of a number of competing models. This provides an alternative for the currently prevalent testing of hypotheses using p-values. Both approaches will be compared and illustrated using case studies. Each case study fits in the framework of the normal linear model, that is, analysis of variance and multiple regression.     

Analysis of optimal dynamic withdrawal policies in withdrawal guarantee products

Guaranteed Minimum Withdrawal Benefits (GMWB) are popular riders in variable annuities with withdrawal guarantees. With withdrawals spread over the life of the annuities contract, the benefit promises to return the entire initial annuitization amount irrespective of the market performance of the underlying fund portfolio. Treating the dynamic withdrawal rate as the control variable, the earlier works on GMWB have considered the construction of a continuous singular stochastic control model and the numerical solution of the resulting pricing model. This paper presents a more detailed characterization of the pricing properties of the GMWB and performs a full mathematical analysis of the optimal dynamic withdrawal policies under the competing factors of time value of fund, optionality value provided by the guarantee and penalty charge on excessive withdrawal. When a proportional penalty charge is applied on any withdrawal amount, we can reduce the pricing formulation to an optimal stopping problem with lower and upper obstacles. We then derive the integral equations for the determination of a pair of optimal withdrawal boundaries. When a proportional penalty charge is applied on the amount that is above the contractual withdrawal rate, we manage to characterize the behavior of the optimal withdrawal boundaries that separate the domain of the pricing models into three regions: no withdrawal, continuous withdrawal at the contractual rate and an immediate withdrawal of a finite amount. Under certain limiting scenarios such as a high policy fund value, the time close to expiry, or a low value of guarantee account, we manage to obtain analytical approximate solution to the singular stochastic control model of dynamic withdrawals.     

Manipulation via merging and splitting in claims problems

In claims problems, we study coalitional manipulations via claims merging and splitting. We characterize (division) rules that are non-manipulable via (pairwise) splitting and that also satisfy standard axioms of equal treatment of equals, consistency, and continuity. And we obtain a similar result for non-manipulability via (pairwise) merging.Received: 22 January 2002, Accepted: 5 February 2003, JEL Classification: C70, C71, D70I am grateful to William Thomson for many helpful comments and suggestions. I also thank Murat Sertel and an anonymous referee for many helpful suggestions for the revision. All remaining errors are mine.     

Convergence of Bayesian learning to general equilibrium in mis-specified models

A central unanswered question in economic theory is that of price formation in disequilibrium. This paper lays the groundwork for a model that has been suggested as an answer to this question in, particularly, Arrow [Toward a theory of price adjustment, in: M. Abramovitz, et al. (Ed.), The Allocation of Economic Resources, Stanford University Press, Stanford, 1959], Fisher [Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press, Cambridge, 1983] and Hahn [Information dynamics and equilibrium, in: F. Hahn (Ed.), The Economics of Missing Markets, Information, and Games, Clarendon Press, Oxford, 1989]. We consider sellers that monopolistically compete in prices but have incomplete information about the structure of the market they face. They each entertain a simple demand conjecture in which sales are perceived to depend on the own price only, and set prices to maximize expected profits. Prior beliefs on the parameters of conjectured demand are updated into posterior beliefs upon each observation of sales at proposed prices, using Bayes’ rule. The rational learning process, thus, constructed drives the price dynamics of the model. Its properties are analysed. Moreover, a sufficient condition is provided, relating objectively possible events and subjective beliefs, under which the price process is globally stable on a conjectural equilibrium for almost all objectively possible developments of history.     

Optimal variance- and efficiency-balanced designs for one- and two-way elimination of heterogeneity

Summary In this paper, a series ofE-optimal non-binary variance balanced (block or row-column) designs and a series ofE-optimal non-binary efficiency balanced (block or row-column) designs are provided in certain broad classes of competing designs. Furthermore, their high efficiencies by the usualA- andD-optimality criteria are shown.     

Blocked-Error-R 2: A Conceptually Improved Definition of the Proportion of Explained Variance in Models Containing Loops or Correlated Residuals

Bentler and Raykov (2000, Journal of Applied Psychology 85: 125–131), and Jöreskog (1999a, http://www.ssicentral.com/lisrel/column3.htm, 1999b http://www.ssicentral. com/lisrel/column5.htm) proposed procedures for calculating R ² for dependent variables involved in loops or possessing correlated errors. This article demonstrates that Bentler and Raykov’s procedure can not be routinely interpreted as a “proportion” of explained variance, while Jöreskog’s reduced-form calculation is unnecessarily restrictive. The new blocked-error-R ² (beR ²) uses a minimal hypothetical causal intervention to resolve the variance-partitioning ambiguities created by loops and correlated errors. Hayduk (1996) discussed how stabilising feedback models – models capable of counteracting external perturbations – can result in an acceptable error variance which exceeds the variance of the dependent variable to which that error is attached. For variables included within loops, whether stabilising or not, beR ² provides the same value as Hayduk’s (1996) loop-adjusted-R ². For variables not involved in loops and not displaying correlated residuals, beR ² reports the same value as the traditional regression R ². Thus, beR ² provides a conceptualisation of the proportion of explained variance that spans both recursive and nonrecursive structural equation models. A procedure for calculating beR ² in any SEM program is provided.     

M-tests in multivariate models

Summary For testing homogeneity in multivariatek sample model, robust tests based onM-estimators are proposed and their asymptoticx ²-distributions are investigated. FurthermoreM-tests in multivariate regression models are discussed.